In the loop: Greatness walks alone

Feb. 1, 2001
Almost 300 years ago, one of the great figures of Western civilization was laid to rest in Hannover, Germany

Almost 300 years ago, one of the great figures of Western civilization was laid to rest in Hannover, Germany. Surely there were other funerals taking place that November day in 1716, but none more significant than this, at least from an historical perspective.

The life that touched so many, then and now, was that of Gottfried Wilhelm von Leibniz, mathematician, philosopher, statesman, and visionary. Born in Leipzig in the summer of 1646, he was the son of a philosophy professor, and the grandson of a prominent lawyer.

Leibniz never had much of a chance to enjoy his privileged youth as his father died when he was only six. He was then sent to the equivalent of a public school, where he received a rudimentary education. On his own, he learned advanced Latin and Greek, and at 14, entered the local university. Within five years, he was a master in mathematics, philosophy, theology, and law; a year later, he received a doctorate in jurisprudence.

For the next 50 years, Leibniz blazed a trail from Nuremberg, Frankfurt, and Mainz, to Paris, London, Rome, Moscow, and Hannover. Along the way, he hobnobbed with every ranking member of society from Louis XIV and George I to Russia’s Peter the Great.

Leibniz, who remained a bachelor, was an avid correspondent, maintaining contact with more than 600 scholars. He would have loved the Internet. The 1903 discovery of over 15,000 letters shows he communicated regularly with Bernoulli, Huygens, Newton, Boyle, Hooke, and Oldenburg to name a few. He was also active among the aristocracy through whom he worked to establish an institutional framework, including the Brandenburg Society and the St. Petersburg Academy of Science.

No project or dream was too big for Leibniz. Talk about ambition – he wanted to collate all human knowledge, reconcile the Catholic and Protestant churches, and unite Eastern and Western math and philosophy. If he needed political pull, he’d make a new friend or elevate one he already had. He even arranged a royal marriage, introducing Princess Charlotte to Rinaldo d’Este, which gave Hannover (his hometown) electoral clout.

His technical accomplishments were equally impressive. As one historian put it, “taking mathematics from its beginning to the time of Newton, what Leibniz has done is much the better half.” Each time you use an integral sign, for example, you’re copying notation Leibniz invented. Same goes for the dot multiplier. “I do not like ‘X’ as a symbol for multiplication, as it is too easily confounded with x,” Leibniz wrote to Johann Bernoulli in reference to his practical notation.

Leibniz, along with Isaac Newton, worked out much of the calculus taught in engineering schools today. Determinants, separation of variables, reduction of homogeneous equations, and the procedure for solving first-order linear equations were all born in Leibniz’s fertile mind.

To Leibniz, calculus was just a tool, a means to an end. Using his own discoveries and what he learned from others, he solved some of the most perplexing problems of his time, delving into motion and dynamics. It’s no surprise he was the first to recognize the special significance of the quantity 1⁄2mv2, linking it to concepts now known as kinetic energy, potential energy, and momentum.

Perhaps because of his own experience, Leibniz was a strong proponent for interdisciplinary study. For that reason, he didn’t care much for universities because their faculty structure prevented the cross-fertilization of ideas which he saw as essential to real progress. I like to think he would have enjoyed this magazine.

Never one for the status quo, Leibniz, in his final public debate, argued that space, time, and motion are relative, opposing the established Newtonian view. Such stands, needless to say, didn’t win him many friends.

Toward the end of his life, Leibniz unloaded his biggest surprise of all in a paper delivered at the Paris Academy of Science. “I enclose an attempt to devise a numerical system that may prove to be completely new. By using a binary system based on the number ‘2,’ I am able to write all numbers in terms of ‘1’ and ‘0.’ I have done this not for mere practical reasons, but rather to allow new discoveries to be made. This system can lead to new information that would be difficult to obtain any other way.”

This was Leibniz at his best – innovative, fresh, and against the grain. And yet it was his undoing. Leibniz was so far ahead of his time, he was often out of step with others.

His funeral was quite modest and only one mourner, his assistant Eckhart, bothered to show up. I doubt this would have bothered the great Leibniz, however. I’m sure he allowed Eckhart to take a break once in a while.

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